3/5x-6=2x+2

Solution for 3/5x-6=2x+2 equation:

3/5x-6=2x+2

We move all terms to the left:

3/5x-6-(2x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-2x-2-6=0

We multiply all the terms by the denominator


-2x*5x-2*5x-6*5x+3=0

Wy multiply elements

-10x^2-10x-30x+3=0

We add all the numbers together, and all the variables

-10x^2-40x+3=0

a = -10; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-10)·3
Δ = 1720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1720}=\sqrt{4*430}=\sqrt{4}*\sqrt{430}=2\sqrt{430}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{430}}{2*-10}=\frac{40-2\sqrt{430}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{430}}{2*-10}=\frac{40+2\sqrt{430}}{-20}
$